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Two-stage multi-innovation stochastic gradient algorithm for multivariate output-error ARMA systems based on the auxiliary model

Author

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  • Qinyao Liu
  • Feng Ding
  • Quanmin Zhu
  • Tasawar Hayat

Abstract

This paper investigates the parameter estimation problem for multivariate output-error systems perturbed by autoregressive moving average noises. Since the identification model has two different kinds of parameters, a vector and a matrix, the gradient algorithm cannot be used directly. Therefore, we decompose the original system model into two sub-models and proceed the identification problem by the collaboration between the two sub-models. By employing the gradient search and determining the optimal step-sizes, we present an auxiliary model based two-stage projection algorithm. However, in order to alleviate the sensitivity to the noise, we reselect the step-sizes and derive the auxiliary model based two-stage stochastic gradient (AM-2S-SG) algorithm. Based on the AM-2S-SG algorithm, an auxiliary model based two-stage multi-innovation stochastic gradient algorithm is proposed to generate more accurate estimates. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed algorithms.

Suggested Citation

  • Qinyao Liu & Feng Ding & Quanmin Zhu & Tasawar Hayat, 2019. "Two-stage multi-innovation stochastic gradient algorithm for multivariate output-error ARMA systems based on the auxiliary model," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(15), pages 2870-2884, November.
    • Handle: RePEc:taf:tsysxx:v:50:y:2019:i:15:p:2870-2884
    DOI: 10.1080/00207721.2019.1690720
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